The exponent of a number claims exactly how many type of times to use the number in a multiplication.

You are watching: I to the power of -1

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In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64

In words: 82 might be referred to as "8 to the power 2" or "8 to the second power", or sindicate "8 squared"

Exponents are additionally referred to as Powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 could be referred to as "5 to the third power", "5 to the power 3" or ssuggest "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 can be dubbed "2 to the fourth power" or "2 to the power 4" or ssuggest "2 to the 4th"

You deserve to multiply any number by itself as many kind of times as you desire making use of exponents.

Try here:

In General

So in general:

an tells you to multiply a by itself,so there are n of those a"s:
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Another Way of Writing It

Sometimes world use the ^ symbol (over the 6 on your keyboard), as it is simple to kind.

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Negative Exponents

Negative? What could be the oppowebsite of multiplying? Dividing!

So we divide by the number each time, which is the exact same as multiplying by 1number


Negative? Flip the Positive!

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That last example verified an less complicated way to handle negative exponents:

Calculate the positive exponent (an)

More Examples:


Negative ExponentReciprocal ofHopeful ExponentAnswer
4-2 = 1 / 42 = 1/16 = 0.0625
10-3 = 1 / 103 = 1/1,000 = 0.001
(-2)-3 = 1 / (-2)3 = 1/(-8) = -0.125

What if the Exponent is 1, or 0?

1If the exponent is 1, then you simply have the number itself (example 91 = 9)
0If the exponent is 0, then you get 1 (instance 90 = 1)
But what around 00 ? It could be either 1 or 0, and so civilization say it is "indeterminate".

It All Makes Sense

If you look at that table, you will certainly see that positive, zero or negative exponents are really component of the same (sensibly simple) pattern: